Find the value of x-y if 57x + 61y = 23 and 61x + 57y = 27
Answers
Solution :-
→ 57x + 61y = 23 ------- Eqn.(1)
→ 61x + 57y = 27 ------- Eqn.(2)
multiply Eqn.(1) by 61 and Eqn.(2) by 57 and subtracting the result we get,
→ 61(57x + 61y) - 57(61x + 57y) = 61*23 - 57*27
→ 3477x - 3477x + 3721y - 3249y = 1403 - 1539
→ 472y = (-136)
→ y = (-136/472)
putting value of y in Eqn.(1)
→ 57x + 61(-136/472) = 23
→ 57x - (8296/472) = 23
→ 57x = 23 + (1037/59)
→ 57x = (2394/59)
→ x = (2394/3363)
then,
→ x - y
→ (2394/3363) - (-136/472)
→ (2394/3363) + (136/472)
→ 2394/(57*59) + (136/59*8)
→ (2394*8 + 7752)/3363*8
→ 26904/3363*8
→ (3363/3363)
→ 1 (Ans.)
Shortcut :-
→ 57x + 61y = 23 ------- Eqn.(1)
→ 61x + 57y = 27 ------- Eqn.(2)
subtracting Eqn.(1) from Eqn.(2)
→ (61x + 57y) - (57x + 61y) = 27 - 23
→ 61x - 57x + 57y - 61y = 4
→ 4x - 4y = 4
→ 4(x - y) = 4
→ (x - y) = 1 (Ans.)
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Given : 57x + 61y = 23 and 61x + 57y = 27
To Find : Value of x - y
Solution:
61x + 57y = 27 Eq1
57x + 61y = 23 Eq2
Eq1 - Eq2
=> 61x + 57y - ( 57x + 61y) = 27 - 23
=> (61x - 57x ) + ( 57y - 61y) = 4
=> 4x + (-4y) = 4
=> 4x - 4y = 4
=> x - y = 1
Value of x - y is 1
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